Understanding the Notation of the Parts Formula

In summary: To integrate a function using integration by parts, you need to find a function that you can integrate and then use that function to integrate the other function.
  • #1
PrudensOptimus
641
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Can someone explain the notation of the parts formula pls.,.. it's very very confusing.


int [u dv] = uv - int [v du]

...

very confuzing, ... made me think it was the product formula lol. And I still don't understand what does dv and dx and all these d stuff standfor in integrals.

they have those dv = 1dx.. i can understand that,... dv/dx = 1, they just moved dx over , but then they made 1/dx = dv... i got confuzed...
 
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  • #2
i think you should look at that equation as so...

∫f(x)g'(x)dx = f(x)g(x)-∫g(x)f'(x)dx

for example a simple integral:

Find ∫x sinx dx.

∫x sinxdx= f(x)g(x)-∫g(x)f'(x)dx

= x(-cosx)-∫(-cosx)dx

= -x cosx + ∫cosx dx

= -x cosx + sinx + C (where C is a Constant m8)


Hope it helped. i can do some more examples if you like. :wink:
 
  • #3
Actually, the "integration by parts" formula should make you think of "product rule" (hopefully without laughing too hard).

Integration by parts is the opposite of using the product rule to differentiate. The product rule says that d(uv)/dx= u dv/dx+ v du/dx

Convert that into "differential form" (if you really have trouble understanding "dv and dx and all these d stuff standfor in integrals" you might want to go back and review the connection between derivatives and differentials): d(uv)= u dv+ v du. Integrating both sides of that gives "integration by parts": uv= int(u dv)+ int(v du) so
int(u dv)= uv- int(vdu).

Typically, an integration by parts problem involves a product of functions to be integrated. You need to select one of them (that you can integrate easily) to be "dv" (with the "dx" from the integral included- integrating dv give you v) and the other (which hopefully you can differentiate) to be "u"- differentiating u gives you du. Notice that integration by parts does not immediately give you the integral- what happens is that it gives you a new integral to do: int(v du). If you can do that, then you can finish the problem so: you need to choose "dv" that you can integrate, "u" that you can differentiate, and, hopefully, so that you can integrate "vdu".

Remember, most elementary functions cannot be integrated in terms of elementary functions!
 

What is the parts formula?

The parts formula is a mathematical equation used to calculate the proportion of a whole that is made up by a certain part or parts. It is commonly used in calculating percentages, ratios, and proportions.

What are the different parts of the parts formula?

The parts formula consists of three parts: the whole, the part, and the percentage or proportion. The whole refers to the total amount, the part refers to the specific amount being considered, and the percentage or proportion represents the relationship between the two.

How do you calculate the parts formula?

The formula for calculating the parts formula is: Part/Whole = Percentage/Proportion. This means that to find the percentage or proportion, you divide the part by the whole. To find the part, you multiply the whole by the percentage or proportion.

What is the significance of understanding the parts formula?

Understanding the parts formula is important in many fields, including science, finance, and business. It allows for accurate and efficient calculations of percentages, ratios, and proportions, which are essential in data analysis and decision making.

What are some real-life applications of the parts formula?

The parts formula is used in various real-life scenarios, such as calculating the percentage of ingredients in a recipe, determining the sales tax on a purchase, and analyzing data in scientific experiments. It is also commonly used in financial analysis, such as calculating profit margins and investment returns.

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